Almost Poisson integration of rigid body systems

Journal Article · Thu Jul 01 04:00:00 EDT 1993 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1993.1128· OSTI ID:441379

Austin, M A; Krishnaprasad, P S ^[1]; Wang, Li-Sheng ^[2]

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1. Univ. of Maryland, College Park, MD (United States)
2. National Taiwan Univ., Taipei (China)

In this paper we discuss the numerical integration of Lie-Poisson systems using the mid-point rule. Since such systems result from the reduction of hamiltonian systems with symmetry by lie group actions, we also present examples of reconstruction rules for the full dynamics. A primary motivation is to preserve in the integration process, various conserved quantities of the original dynamics. A main result of this paper is an O(h{sup 3}) error estimate for the Lie-Poisson structure, where h is the integration step-size. We note that Lie-Poisson systems appear naturally in many areas of physical science and engineering, including theoretical mechanics of fluids and plasmas, satellite dynamics, and polarization dynamics. In the present paper we consider a series of progressively complicated examples related to rigid body systems. We also consider a dissipative example associated to a Lie-Poisson system. The behavior of the mid-point rule and an associated reconstruction rule is numerically explored. 24 refs., 9 figs.

• OSTI ID: 441379
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 107; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
COMPUTERIZED SIMULATION
DYNAMICS
FLUID FLOW
ITERATIVE METHODS
MECHANICS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS